We present a simple, efficient, and scalable unfolding network, SAUNet, to simplify the network design with an adaptive alternate optimization framework for hyperspectral image (HSI) reconstruction. SAUNet customizes a Residual Adaptive ADMM Framework (R2ADMM) to connect each stage of the network via a group of learnable parameters to promote the usage of mask prior, which greatly stabilizes training and solves the accuracy degradation issue. Additionally, we introduce a simple convolutional modulation block (CMB), which leads to efficient training, easy scale-up, and less computation. Coupling these two designs, SAUNet can be scaled to non-trivial 13 stages with continuous improvement. Without bells and whistles, SAUNet improves both performance and speed compared with the previous state-of-the-art counterparts, which makes it feasible for practical high-resolution HSI reconstruction scenarios. We set new records on CAVE and KAIST HSI reconstruction benchmarks. Code and models are available at this https URL.